To solve the problem we must know about the exponential function of growth.
An exponential function of Growth shows the decrement of something from the original value after every period of time such that the decrement is at a constant rate.
[tex]y=x(1+r)^t[/tex]
where,
y is the value after t period of time at a decrement rate of r and x is the initial amount.
Given to us
Comparing the exponential function,
we understand that in function, [tex]y=10(1+0.4)^t[/tex],
y is the amount after growth of t years,
10 is the initial amount,
0.4 = 40% is the rate of growth.
Hence, the initial amount a is 10, and the rate of growth r is 40% in the given exponential function.
For t = 5,
[tex]y=10(1+0.4)^t[/tex]
substituting the values,
[tex]y=10(1+0.4)^5\\\\y = 10 \times 5.37824\\\\y = 53.7824\approx 53.79[/tex]
Hence, the amount after 5 years will be 53.79.
Learn more about Exponential function of growth: https://brainly.com/question/11743945
